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2 years ago

A man drives 500 metres up a road which is inclined at 30° to the horizontal. How

Mathematics

1 answer:

Basile [38]2 years ago

6 0

Step-by-step explanation:

Height = 500sin30° = 500(0.5) = 250.

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2 years ago

Find the integral, using techniques from this or the previous chapter.<br> ∫x(8-x)3/2 dx

Soloha48 [4]

Answer:

$\int x(8-x)^{3/2}dx= -\frac{16}{5} (8-x)^{\frac{5}{2}} +\frac{2}{7} (8-x)^{\frac{7}{2}} +C$

Step-by-step explanation:

For this case we need to find the following integral:

$\int x(8-x)^{3/2}dx$

And for this case we can use the substitution $u = 8-x$ from here we see that $du = -dx$ , and if we solve for x we got $x = 8-u$ , so then we can rewrite the integral like this:

$\int x(8-x)^{3/2}dx= \int (8-u) u^{3/2} (-du)$

And if we distribute the exponents we have this:

$\int x(8-x)^{3/2}dx= - \int 8 u^{3/2} + \int u^{5/2} du$

Now we can do the integrals one by one:

$\int x(8-x)^{3/2}dx= -8 \frac{u^{5/2}}{\frac{5}{2}} + \frac{u^{7/2}}{\frac{7}{2}} +C$

And reordering the terms we have"

$\int x(8-x)^{3/2}dx= -\frac{16}{5} u^{\frac{5}{2}} +\frac{2}{7} u^{\frac{7}{2}} +C$

And rewriting in terms of x we got:

$\int x(8-x)^{3/2}dx= -\frac{16}{5} (8-x)^{\frac{5}{2}} +\frac{2}{7} (8-x)^{\frac{7}{2}} +C$

And that would be our final answer.

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2 years ago